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I have been speculating upon this: we say that a conic-section is a curve made by the intersection of a plane and a double cone. On the same lines can we say that a conicoid is a surface made by the intersection of a 3-dimensional space and a 4-dimensional double hypercone? If so, can both the results be derived analytically , for instance, we have the equations of a double cone and a plane and hence we show that the locus of their intersection is a conic-section? Any help is welcome. Thanks!

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Okay. By now I have learnt that my guessing is right( that a conicoid is a surface made by the intersection of a 3-dimensional space and a 4-dimensional double hypercone) but I still desire to have a rigorous treatment for the general case of intersection of an n-dimensional hyperspace with a (n+1) dimensional hypercone. I mean some reference where I can find related theorems.

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Awe Kumar Jha
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  • @Blue, my question is a bit different for I am focusing on an analytic derivation which I can generalise to n-dimensions . – Awe Kumar Jha Dec 23 '18 at 08:31
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    You should edit your question to reference the question in my comment, and clearly describe how your interest differs. (I'm not saying it doesn't. I'm just saying: Don't rely on readers to see your comment. Include that information in the question itself.) Also, you mention that you "have learnt that my guessing is right". Could you explain exactly what "guessing" you mean here, and what exactly you have already "learnt"? This will help responders avoid wasting time telling you things you already know. – Blue Dec 23 '18 at 08:41

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